數學圖形之地形曲面

      在數學表達式中,若是能寫成這種形式:y = f(x, z),就能夠稱之爲地形曲面.由於能夠認爲每個平面上的位置都會對應惟一一個高度值.

      在這一節中,將展現幾個地形曲面的圖形.使用本身定義語法的腳本代碼生成超球圖形.相關軟件參見:數學圖形可視化工具,該軟件免費開源.QQ交流羣: 367752815

      這個軟件的最第一版本就是隻針對y = f(x, z)這種方程而寫的,詳見:WHY數學圖形顯示工具.當時是輸入一個數學表達式,而後再輸入其數據範圍來生成一個圖形,以下圖所示:

 

然後在這個軟件的基礎上,作了重構.重寫了原有的數學表達式解析的算法.本身定義了一套腳本語言格式,以腳本的形式編輯數學圖形.

(1)

#http://www.mathcurve.com/surfaces/algebricsu/algebricsu.shtml

vertices = dimension1:101 dimension2:101

x = from (-4) to (4) dimension1
z = from (-4) to (4) dimension2

a = (x*x + z*z)

y = x*z/(a*a)

y = limit(y, -5, 5)

(2)

vertices = dimension1:320 dimension2:320

x = from (-4) to (4) dimension1
z = from (-4) to (4) dimension2
r = x^2 + z^2
y = sin(x^2 + z^2*3)/(0.05 + r) + (x^2 + z^2*5)*exp(1 - r)/2

u = x
v = z

x = x*5
y = y*5
z = z*5

(3)

vertices = dimension1:201 dimension2:201
x = from (-20) to (20) dimension1
z = from (-20) to (20) dimension2

y = sin(sqrt(x*x+z*z))

u = x/5
v = z/5

(4)

vertices = dimension1:201 dimension2:201
x = from (-8*PI) to (8*PI) dimension1
z = from (-8*PI) to (8*PI) dimension2
a = abs(x)
b = abs(z)
y = sin(a * b * 0.1)*exp((a + b)/24)

u = x/5
v = z/5

(5)

vertices = dimension1:201 dimension2:201

x = from (-100) to (100) dimension1
z = from (-100) to (100) dimension2
y = sqrt(abs(x*z)) + sin(x*z*0.005)*5

u = x/10
v = z/10

(6)

vertices = dimension1:101 dimension2:101

x = from (-100) to (100) dimension1
z = from (-100) to (100) dimension2
y = sqrt(abs(x*z))

u = x/10
v = z/10